A Direct Algorithm for Pole Placement by State-derivative Feedback for Single-input Linear Systems

This paper deals with the direct solution of the pole placement problem for single-input linear systems using state-derivative feedback. This pole placement problem is always solvable for any controllable systems if all eigenvalues of the original system are nonzero. Then any arbitrary closed-loop poles can be placed in order to achieve the desired system performance. The solving procedure results in a formula similar to the Ackermann formula. Its derivation is based on the transformation of a linear single-input system into Frobenius canonical form by a special coordinate transformation, then solving the pole placement problem by state derivative feedback. Finally the solution is extended also for single-input time-varying control systems. The simulation results are included to show the effectiveness of the proposed approach

The Relationship between Trauma due to Winter Storm Alexa, PTSD, Mental Health of Palestinians in the Gaza Strip

Aim: This study investigated the relationship between trauma due to winter storm Alexa, PTSD and other mental health problems of Palestinian in Gaza Strip. Method: The sample consisted of 105 males (50%) and 105 females (50%) selected from three of the most affected areas by flooding in 2014 due to Alexa storm in Gaza Strip. Participants age range was 20-65 years, with a mean age 40.88 (SD = 9.8), with a mean age of years. Mental health status was assessed by a sociodemographic scale, the Trauma Due to Flood Scale, PTSD scale, and General Health Questionnaire (28 items). Results: Mean traumatic events experienced were 7.8. There were no statistically significant differences between males and females in reporting traumatic events. Mean post-traumatic stress disorder was 18.65, re-experiences symptoms was 6.4, avoidance symptoms was 5.7 and mean arousal symptoms was 5.73. The study showed that 34.8% reported full criteria of PTSD. There were no statistically significant differences in PTSD total scores and subscales and sex of participants. Mean GHQ-28 was 12.12, somatization mean was 3.21, anxiety was 3.31, social dysfunction was 3.34, and depression was 2.27, 91% of the participants were rated as psychiatric morbidity cases and need further investigation. Males significantly scored more in social dysfunction than females. Traumatic events were significantly correlated with PTSD and general mental health and all subscales. Conclusion and implications: This study has important implications for need of establishing and implementing psychosocial intervention programs for in the Gaza Strip not only for those victims of political violence but also for people exposed to other types of traumatic events such as natural disasters

Eigenstructure Assignment by State-derivative and Partial Output-derivative Feedback for Linear Time-invariant Control Systems

This paper introduces a parametric approach for solving the problem of eigenstructure assignment via state-derivative feedback for linear control time-invariant systems. This problem is always solvable for any controllable systems if the open-loop system matrix is nonsingular. In this work, the parametric solution to the feedback gain matrix is introduced that describes the available degrees of freedom offered by the state-derivative feedback in selecting the associated eigenvectors from an admissible class. These freedoms can be utilized to improve the robustness of the closed-loop system. Finally, the eigenstructure assignment problem via partial output-derivative feedback is introduced. Numerical examples are included to show the effectiveness of the proposed approach

Minisum and minimax transfer point location problem with random demands points

This paper is concerned with analyzing some models of the weighted transfer point location problem under the minisum and minimax criterions when demand points are randomly distributed over regions of the plane and the location of the service facility is known. In case of minisum objective with rectilinear distance, an iterative procedure was constructed for estimating the optimal transfer point location using the hyperbolic application procedure. Exact analytic solution was obtained when the random demand points follow uniform distributions. A unified analytic optimal solution was provided for all types of probability distributions of the random demand points when the distance is the squared Euclidean distance. For minimax objective with squared Euclidean distance, an iterative procedure based on Karush-Kuhn-Tucker conditions was developed to produce an approximate solution to the optimal solution. Illustrative numerical examples were provided

A Complete Parametric Solutions of Eigenstructure Assignment by State-Derivative Feedback for Linear Control Systems

In this paper we introduce a complete parametric approach for solving the problem of eigenstructure assignment via state-derivative feedback for linear systems. This problem is always solvable for any controllable systems iff the open-loop system matrix is nonsingular. In this work, two parametric solutions to the feedback gain matrix are introduced that describe the available degrees of freedom offered by the state-derivative feedback in selecting the associated eigenvectors from an admissible class. These freedoms can be utilized to improve robustness of the closed-loop system. Accordingly, the sensitivity of the assigned eigenvalues to perturbations in the system and gain matrix is minimized. Numerical examples are included to show the effectiveness of the proposed approach.

Unbounded Perturbations of the Generator Domain

Let X, U and Z be Banach spaces such that Z in X (with continuous and dense embedding), L : Z ->X be a closed linear operator and consider closed linear operators G, M : Z -> U. Putting conditions on G and M we show that the operator A = L with domain D(A) ={z∈Z: Gz=Mz} generates a C0- semigroup on X. Moreover, we give a variation of constants formula for the solution of an inhomogeneous problem. Several examples will be given, in particular heat equation with distributed unbounded delay at the boundary condition

Cross-layer distributed power control: A repeated games formulation to improve the sum energy-efficiency

The main objective of this work is to improve the energy-efficiency (EE) of a multiple access channel (MAC) system, through power control, in a distributed manner. In contrast with many existing works on energy-efficient power control, which ignore the possible presence of a queue at the transmitter, we consider a new generalized cross-layer EE metric. This approach is relevant when the transmitters have a non-zero energy cost even when the radiated power is zero and takes into account the presence of a finite packet buffer and packet arrival at the transmitter. As the Nash equilibrium (NE) is an energy-inefficient solution, the present work aims at overcoming this deficit by improving the global energy-efficiency. Indeed, as the considered system has multiple agencies each with their own interest, the performance metric reflecting the individual interest of each decision maker is the global energy-efficiency defined then as the sum over individual energy-efficiencies. Repeated games (RG) are investigated through the study of two dynamic games (finite RG and discounted RG), whose equilibrium is defined when introducing a new operating point (OP), Pareto-dominating the NE and relying only on individual channel state information (CSI). Accordingly, closed-form expressions of the minimum number of stages of the game for finite RG (FRG) and the maximum discount factor of the discounted RG (DRG) were established. The cross-layer model in the RG formulation leads to achieving a shorter minimum number of stages in the FRG even for higher number of users. In addition, the social welfare (sum of utilities) in the DRG decreases slightly with the cross-layer model when the number of users increases while it is reduced considerably with the Goodman model. Finally, we show that in real systems with random packet arrivals, the cross-layer power control algorithm outperforms the Goodman algorithm.Comment: 36 pages, single column draft forma

Diagonals of rational functions, pullbacked 2F1 hypergeometric functions and modular forms (unabrigded version)

We recall that diagonals of rational functions naturally occur in lattice statistical mechanics and enumerative combinatorics. We find that a seven-parameter rational function of three variables with a numerator equal to one (reciprocal of a polynomial of degree two at most) can be expressed as a pullbacked 2F1 hypergeometric function. This result can be seen as the simplest non-trivial family of diagonals of rational functions. We focus on some subcases such that the diagonals of the corresponding rational functions can be written as a pullbacked 2F1 hypergeometric function with two possible rational functions pullbacks algebraically related by modular equations, thus showing explicitely that the diagonal is a modular form. We then generalise this result to eight, nine and ten parameters families adding some selected cubic terms at the denominator of the rational function defining the diagonal. We finally show that each of these previous rational functions yields an infinite number of rational functions whose diagonals are also pullbacked 2F1 hypergeometric functions and modular forms.Comment: 39 page

Hydrogenolysis of Glycerol over γ-Al2O3-Supported Iridium Catalyst

In recent years, much attention has been focused on the hydrogenolysis of biodiesel derived glycerol to other high value products for the sustainable development and efficient valorization strategies. In the present work, alumina-supported Ir catalyst was prepared by the incipient wetness impregnation method and tested in the glycerol hydrogenolysis reaction. The synthesized catalyst was characterized by neutron activation analysis, N2 physisorption, and H2 chemisorption techniques. The experiments standard conditions were 150 mL feed volume, 0.3 g catalyst, 1500 rpm stirring speed, and 5 wt% glycerol aqueous solution for 4 h. The effects of catalyst amount, temperature, hydrogen pressure, stirring speed, and solution pH on glycerol conversion and selectivity of the principal products obtained were also investigated. The glycerol conversion and the 1,2-propanediol selectivity varied from 4.9% to 22% and from 23.8% to 70.3%, respectively. It was found that the selectivity of 1,2-propanediol increased significantly with the increased alkalinity of the reaction medium